The current research in the Laboratory for Stochastic Systems focuses on the areas of modeling, optimization and control of stochastic systems, such as transportation, production/inventory and supply chain networks. Such systems are dynamic and they operate under internal and external uncertainties, which are generally considered to be large-scale and complex. We are interested in developing new models that will realistically represent complex phenomena such as congestion, traffic flow randomly interrupted by incidents, or retailer’s behavior when selling substitutable products. Here are the main research topics and some details:

Transportation - Traffic Congestion

Research Statement: Our research aims to develop a tool for providing information on how many vehicles are expected to be in a road at any given time or during specific events, such as inclement weather or incident recovery periods. The model incorporates the flow during congestion due to incidens.It also contributes to mapping systems to give route options to commuters by taking into risk of delay opposed to conventional planners.

Models and Methodologies

• Incident distribution over the network
• Statistical Analysis
• Impact of incidents on the traffic flow
• Queueing Theory Models
• Optimal incident management
• Emergency Vehicle Dispatching
• Traffic Diversion to minimize Congestion
• Computer Simulation & Response Surface Methodology
• Stochastic Programming

Research Statements:

• Enabling extraction of travel time reliability indices without the need for simulation or extensive data collection
• Proposing models for probability distributions of traffic parameters (travel time and traffic density) with limited data

Some Related Publications:

• Probabilistic programming models for traffic incident management operations planning
• Evaluation of Incident Management Strategies and Technologies using an Integrated Traffic/Incident Management Simulation
• Modeling Traffic Flow Interrupted by Incidents
• Evaluation of Incident Management Strategies and Technologies using an Integrated Traffic/Incident Management Simulation

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Transportation - Railway Maintenance

● Predictive maintenance scheduling in railway systems

Research Statement: Our objective is to develop a decision support tool that produces an efficient maintenance schedules. In order to obtain an efficient schedule, data-driven defect amount and location prediction module is created that minimizes the false negative defect rate. This prediction model is embedded in a Markovian Decision Process that proposes the optimal maintenance policy for a planning horizon. These policies are then embedded in the short-term maintenance scheduling approach.

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Production Inventory Systems

• Production Control of a Manufacturing System
• Maintenance Policies for Repairable Machines
• Production Control of a Two-Stage Manufacturing System
• Substitutable Products Inventory Management
• Price-Setting Newsvendor Problem under Mean-Variance Criterion
  Research Statement: We consider the single-product, single-period newsvendor problem. Our main goal is to study how risk-sensitive individuals change their decisions under price-dependent demand when the demand conditions.We model this problem as a mean-variance tradeoff problem, where relative weights are assigned to the mean and the variance.Our work is specifically focuses on finding the conditions under which this problem has a unique optional solution.

Some Related Publications:

• On the Unimodality of the Price-Setting Newsvendor Problem with Additive Demand Under Risk
• Price-Setting Newsvendor under Mean-Variance Criterion
• Inventory Control under Substitutable Demand: A Stochastic Game Application
• Forecasting for Inventory Planning in Supply Chains
• Maintenance of Infinite-Server Service Systems subjected to Random Shocks

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Game Theory and Games for Infrastructure Security (For more details, visit GRIST LAB)

Research Statement: We consider network protection games where an adversary and a defender compete with each other within the context of a game. Our objective is to develop game theoretic models that consider environmental uncertainty, information asymmetry and dynamic environment. From a development point of view we want to develop a virtual game built inside an immersive virtual world designed to both collect data about the players' behavior (defender, adversary, and people) and to validate the game models using metrics such as the expected damage, the fraction of unsuccessful attacks, etc.

Some Related Publications:

• Urban Rail Patrolling: A Game Theoretic Approach
• A Robust Approach to Infrastructure Security Games
• A Game Theoretic Analysis of Secret and Reliable Communication with Active and Passive Adversarial Modes
• Security Games with Unknown Adversarial Strategies

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Foundations of Stochastic Decision Analysis

• Theoretical Foundations
• Stochastic Optimization and Control
• Markov Decision Processes
• Semi-Markov Decision Processes
• Stochastic Dynamic Programming
• Game Theory
• Competitive Zero-Sum, Non-Zero-Sum Games
• Stochastic Games
• Multiple Retailer Inventory Games

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